A complete mathematical derivation showing how Kendall's tau emerges from the copula integral formula τ = 4∫₀¹∫₀¹C(u,v)dC(u,v) - 1
Exploring the fundamental connection between likelihood ratio tests and chi-square distributions through Wilks' theorem, with formal proofs and practical examples.
A comprehensive derivation showing that when testing a single linear contrast in regression, the squared t-statistic equals the corresponding F-statistic, including detailed proofs of variance properties and constraint sum of squares.
Here continues to dive into the mathematics crucial for effective GSEA analysis and machine learning applications in bioinformatics.
Here continues to dive into the mathematics crucial for effective GSEA analysis
Learn why using all genes with proper ranking statistics is crucial for GSEA analysis, and get ready-to-use R code for different differential expression tools.